Question

Find the zeroes of the quadratic polynomial x2-3x-4 and the verify therelationship between the zeroes and the coefficient of the polynomial​

Answer 1

Given:

A quadratic polynomial x²-3x-4

To Find:

• Zeroes of polynomial x²-3x-4

Solution:

Let the given polynomial be

p(x)= x²-3x-4

And x be the zero of the given polynomial, then it will satisfy the polynomial or when we put x in given polynomial then p(x) becomes 0.

i.e. p(x)= x²-3x-4= 0

⇒ x²-3x-4= 0

On splitting the middle terms, we get

⇒ x²-4x+x-4= 0

⇒ x(x-4)+1(x-4)= 0

⇒ (x+1)(x-4)= 0

⇒ x= -1, 4

So, -1 and 4 are the zeroes of the given polynomial.

Verification:

We know that,

For a quadratic polynomial,

$\sf\pink{(A)Sum\:of\:Zeroes=-\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2}}}$

$\sf\purple{(B)Product\:of\:Zeroes=\dfrac{Constant\:Term}{Coefficient\:of\:x^{2}}}$

Therefore,

$\bf\green{\underline{\underline{Verification\:of\:A}}}$

$\sf\pink{4-1=-\dfrac{(-3)}{1}}$

$\sf\pink{3=3}$

Since, L.H.S= R.H.S.

A is verified

$\bf\green{\underline{\underline{Verification\:of\:B}}}$

$\sf\purple{4(-1)=\dfrac{(-4)}{1}}$

$\sf\purple{-4=-4}$

Since, L.H.S= R.H.S.

B is verified

Hence, Zeroes of given polynomial are -1 and 4.

Answer 2

$\Huge\fbox{\color{red}{Hello:-}}$

$\huge\mathfrak\red{Question}$

Find the zeroes of x^2+3x-4

$\color{Green}{\large\underline{\underline\mathtt{Answer:-}}}$ ☞

The graph of p(x) is given above.

Clearly, from the graph x=−4,1 are zeros of p(x).

Verification:-

p(−4)=(−4)2+3×−4−4=16−12−4=0

p(1)=(1)2+3×1−4=1+3−4=0